Consider a floating rate bond with the following characteristics. The bond has just been issued. It has a face value of 1,000 and 3 years time to maturity. Coupons are paid in one, two and three years from now. Each coupon is fixed one year before it is paid, and the coupon is equal to the current yield to maturity of U.S. government bond with a maturity of one year. For example, the coupon to be paid in three years time is equal to the U.S. government bond yield in two years time. Ignore the default risks.

(1) Show that the bond must have a market value of 1,000 today, one year from now and two years from now.

(2) Compare the risks of the floating rate bond with those of a bond that pays fixed coupon, assuming that both bonds have the same maturity and the same issuer.